Marc, we know it as "the bent stick method". A meter length of flex track, a length of hardboard or Masonite, or doorskin, or even a long stainless steel ruler on edge, will accomplish the same sort of curve with minor variations.
Crandell
I never tried to calculate easement on curve,I find it out of purpose for or small trains, but I must admit, I didn't like mathemetics.
I use a very simple and so easy method, the yard stick design track.
See more info's about it and pictures on www.aorailroad.com, the layout of mister David Stewart.
He use this very easy and effective method.
The yarstick is a fine piece of wood, whith a lot of flexibility.
A few points traced whith a pencil, as check point, put in alignement and keep in place whith a few nuts and his flexibility allow gentle curves and the easement comes naturaly.
The flowing of the track is amazing; I use it in Nscale since the expansion of my layout whith great results.
Marc from Belgium
one more drawing:
Paul
Here is a crude hand-drawn image showing what Paul is saying. Note that at the apex of the curve, the radius is matched between the perfectly circular curve and the eased curve. In fact, in this example, it is quite extensive...the range over which they share the same radius at the top of the curve. However, as the eased curve begins to diverge slightly, showing how its radius is changing to a wider one, you can see that it has still not reached the 90 degree point of tangency until past the point, on each side, where the fixed radius curve has turned precisely 90 degrees.
Not all curves are 90 degree curves, but you get the idea how an eased curve must be slightly/somewhat longer than a curve of fixed radius when they otherwise are tangent in parallel lines. The two red lines make that clear...as crude as this depiction is.
Hi gentlemen,
Doc 's information is not spot on. Any curve with a larger radius is working like an easement. The question remains if this is really working when the "new" radius is only a tad larger then the original one.
Working can be seen from a visual point ( nice looking track and gentle leaning into the curve of a train) or from an operational point of view (less derailments).
The easement by Doc requires an extra length of about half an inch and has an offset of about 1/120 part of an inch. I am not sure if this is even visible.
More common in model railroading is an extra required length (= half the total length of an easement) between the length of your longest piece of equipment or half of it. The offset can be calculated with the formula: offset = (L x L) / (24 x R); L = the total length of the easement and R= radius.
An example
when operating 70 ft long cars on a 30" radius the extra required length in HO will be between 5" and 10". So the total length of the easement is between 10" and 20". The matching offset is between 0,14 and 0,28 inch.
The math might seem difficult, laying out easements on subroadbed is rather easy when using flextrack. You just have to allow for the extra required length and the matching offset. The flextrack will form the easement by itself. When drawing, the offset is to small to be noticable anyway; so adding some length is all you have to do. Lance Mindheim always leaves 6" between a turnout and a curve. Those 6" are the extra required length, hence half the total length of his easement. BTW his plans are usually based on 24" radii and 60 ft long cars.
From a visual point of view any easement is better then none. Keeping speeds down is a very sound way to prevent possible derailments. However long modern freightcars and passenger equipment might behave badly on tight curves. Sometimes easements are more then just looking good.
SmilePaul
One could just add a short larger radius segment of curve to each end of a regular radius curve.For example, I find adding a 15 degree 32 in radius curve to a 30 in radius curve is a close approximation to an easement curve created by WinRail.
Co-owner of the proposed CT River Valley RR (HO scale) http://home.comcast.net/~docinct/CTRiverValleyRR/
As Crandell indicated, easements are more important with the smaller radius curves (i.e. 18 - 24) than larger radius situations. How are they "important"?
Well, mechanically its easier on the longer cars and close coupled ones to transfer from tangent to the curve. Trains will make the transition more smoothly and successfully at higher rates of speed. Of course, a big attraction of easements is that they just make for a much better looking and more realistic piece of trackage.
Most of us recall the Lionel or Flyer layouts of our youth, and how those big locos would slam into the sudden curves, and barely stay on the track (if they did at all).............
ENJOY !
Mobilman44
Living in southeast Texas, formerly modeling the "postwar" Santa Fe and Illinois Central
Are easements necessary? I would say it depends on what you feel is important on your layout. From an operational standpoint, probably not. However, they do lead your larger steam locos and rolling stock into the curve, better than without. From the standpoint of making your layout look real, than yes, (at least to me) easements are visually required to make your layout look right.
However, it is your layout and only you get to make the decision on whether to use easements; or, not!
NP 2626 "Northern Pacific, really terrific"
Northern Pacific Railway Historical Association: http://www.nprha.org/
Santa Fe all the way!Sorry if this a stupid question, but ate easements necessary?
Necessary? As your curves tighten and their radii begin to match the length of the longest cars on them, or near the restrictions of movement of the couplers imposed by their mounting design, and as your speeds near scale supersonic, most of us would probably elect to have some form of eased curve. As curves widen, though, and the couplers are not going to be forced against their left and right azimuthal range, and your speeds drop to a scale 80 mph or so, you would find that the easements become more charming as visually appealing and more prototypically correct IF you are modelling...and not just a person who prefers to lay down track and run trains until supper time.
That's a long way to say that it is usually a personal choice, just like 'most everything to do with this hobby, but the majority would want them when the engineering suggests they'll offer some relief from derailments.
as always, it depends.
When running shorter cars or engines with limited speeds you don't.
When I was starting to lay track and roadbed on my layout, instead of laying out the easement for every curve on my sub road bed, I drew a semi circle (half circle) with the easement and a short (6 inch) length of tangent drawn out at one end. I used 22 inches as my minimum radius. I drew this all onto a piece of 1/4 inch plywood and cut the tangent, easement and 1/2 circle with a band saw (It could be cut out with a scroll saw or saber saw or keyhole saw, also). I also cut a notch where the center of the circle was located, so I could place this point, where I knew the center of the curve would be. I sanded the sawn edge of this plywood template to smooth out the edge and used this as a template for drawing the center-lines of my curves. When I needed an easement and tangent to come out of the curve, flipping the template over gave me this feature. I found this template to be very helpful at that point in the construction of my layout.
Re: your 2007 post about easement curves--
(I believe) because I am not a Model Railroader subscriber, I cannot open the link you originally provided in your post, (http://trains.com/mrr/default.aspx?c=a&id=290). Would you happen to know what month/year that article originally appeared in MR so I can find a back issue through Kalmbach or at my library? Overkill or not, I am researching everything I can get my hands on regarding easement curves and superelevation before I start benchwork.
Your help would be most appreciated. Thank you.
(I believe) because I am not a Model Railroader subscriber, I cannot open the link you originally provided, (http://trains.com/mrr/default.aspx?c=a&id=290). Would you happen to know what month/year that article originally appeared in MR so I can find a back issue through Kalmbach or at my library? Overkill or not, I am researching everything I can get my hands on regarding easement curves and superelevation before I start benchwork.
cordon wrote: ..snip.. It seems that very few layouts have double track mains, yet I view them as a "standard," with anything less being a bad compromise. I've planned double track from the beginning. I also feel that trains should run on the right-hand track of the double track mains, except in very special cases.
..snip.. It seems that very few layouts have double track mains, yet I view them as a "standard," with anything less being a bad compromise. I've planned double track from the beginning. I also feel that trains should run on the right-hand track of the double track mains, except in very special cases.
I presume that you consider two sovereign island nations and a continent to be special cases. My double track won't even be signaled for right-hand running.
Back to easements, my research for this thread didn't discover any "easement sections" for sectional track. The old Lionel and American Flyer track didn't come with easements, either. I wonder why the manufacturers don't make them?
Lionel, American Flyer and the current sectional track is meant to be used for TOY TRAINS, not serious model railroads, the same reason that Power Wheels cars don't have working speedometers.
Back when, a MMR who will remain nameless inserted sections of 1.5 X minimum radius and 3 X minimum radius to provide easements of a sort. It was a small improvement over nothing.
Here are some more links: one, two, three (included under two, in case you missed it), four.
Thanks for the data.
Chuck (modeling Central Japan in September, 1964 - to JNR standards, including left hand running)
Oooohhhmmm Oooohhhhmmmm?
Doesn't that have something to do with volts and amperes?
".....I tend to construct double track main lines...."
I'm glad to hear that. It seems that very few layouts have double track mains, yet I view them as a "standard," with anything less being a bad compromise. I've planned double track from the beginning. I also feel that trains should run on the right-hand track of the double track mains, except in very special cases. There have been several very ugly fatal crashes due to running 1:1 trains on the left-hand track.
From the far, far reaches of the wild, wild west I am: rtpoteet
R. T. POTEET wrote: tomikawaTT wrote: With all due respect to Linn Westcott, who was a true model railroading pioneer as well as a long-time employee of Kalpubco, unless you are laying out full-scale curves to be used by Acela, TGV or the Shinkansen the techniques and templates in that article are a gross overkill!Gotta take exception with you on this one there, tomikawaTT.I can get an N Scale 85 foot passenger car with body-mounted couplers to EASE into and out of a 9 inch radius curve - it looks like aitch on a curve of that radius but it will negotiate it - at speed and only experience an occasional trouble; if I try to LURCH an 85 foot passenger car with body-mounted couplers into or out of that 9 inch radius curve I will almost guarantee you that I am going to have troubles.
tomikawaTT wrote: With all due respect to Linn Westcott, who was a true model railroading pioneer as well as a long-time employee of Kalpubco, unless you are laying out full-scale curves to be used by Acela, TGV or the Shinkansen the techniques and templates in that article are a gross overkill!
With all due respect to Linn Westcott, who was a true model railroading pioneer as well as a long-time employee of Kalpubco, unless you are laying out full-scale curves to be used by Acela, TGV or the Shinkansen the techniques and templates in that article are a gross overkill!
Methinks you misunderstood ME, pardner. I am a big advocate of easements - in fact my mountain-country railroad can be accurately described as a bunch of curves connected by easements with an occasional tangent. My point was that it doesn't take number-crunching with an old plugboard IBM mainframe to create a visually attractive and operationally effective easement.
By using my method, I can locate a curve center without wondering what offset a template will give me. That one variable is what turned me off to templates clear back when this article was first published.
Chuck (modeling Central Japan in September, 1964 - with easements)
When you say "slide template along tangent towards the arc until the curve of the easement blends with the arc, " the "curve" that your refer to is that the line marked "center line of track on spiral" on template C from the link in my original post ?
Paste the template to a poster board. Carefully cut along the BLACK LINE. That is the tangent track center line followed by the easment center line. I usually extend the tangent center line a little more for acuracy.
The "curve" is the center line of the easement track which will then blend into the center line of the arc you are entering from the easement.
The beauty of this KISS method is that it only takes only a minute to draw each one. For example, if using 30 inch radius curve, measure 30 1/2 inches from the tangent 90 degrees from the center line as far along as necessary to place the curve where you want it to be. The same as if you are not using an easement. Draw as much of the curve as you want including starting at a point just before the 90 degree point of the tangent.
Place the template tangent side along the tangent line and then slide it along until the easement curve blends with the 30 inch radius curve you have already drawn.
Do one and the rest will go like clockwork.
BigRusty wrote: If you don't draw the center line for ALL of the track you are going to lay before you do ANTHING else, you are asking for trouble. It is a lot easier to erase a pencil line than to tear up already laid track.If you are using cork roadbed this is an absolute MUST because each half of the roadbed must be set to the centerline. Draw the tangent. Draw the arc offset 1/2 inch. Set the tangent end of the template along the tangent already drawn. Then SLIDE it along the tangent toward the arc until the curve of the easment blends with arc.Believe, me. This is the fastest, and most accurate way to create a spiral easement from one that has been mathematically calculated, and true to propotype.
If you don't draw the center line for ALL of the track you are going to lay before you do ANTHING else, you are asking for trouble. It is a lot easier to erase a pencil line than to tear up already laid track.
If you are using cork roadbed this is an absolute MUST because each half of the roadbed must be set to the centerline.
Draw the tangent. Draw the arc offset 1/2 inch. Set the tangent end of the template along the tangent already drawn. Then SLIDE it along the tangent toward the arc until the curve of the easment blends with arc.
Believe, me. This is the fastest, and most accurate way to create a spiral easement from one that has been mathematically calculated, and true to propotype.
cheers
OOhhmmmmm.... OOhhmmmmm:
Grasshopper, to be at ease with your inner spiral you must clear your mind
See the tangent....
Be the tangent....
Find your Center... line...
OOhhmmmm.... OOhhmmmmm
Yes, that's the way to do it. Just remember that the tangent must be planned all along for a position where it will lead into the easement and still afford you your desired radius at the midpoint of the curve proper. So, in real live terms, railroads are really a series of sinuous and carefully measured curves between which tangents are drawn. Neat way of looking at them after that realization.
As stated earlier, probably the least troublesome, and just as pragmatic and effective way to generate an eased curve is by pegging the first 6" of a section of flextrack to immobilize it along the tangent centreline, and then force the free end to conform to your curve near its midpoint. Your easement will appear naturally between these extremes, the fixed end and the forced end. Trust us on this one!
cordon wrote: This is really hard to grasp without a diagram, so I will give you a diagram.I agree with Dave. I use a piece of flextrack to form the shape of the curve between the point on the tangent track and the point on the curve. I use the "midpoint" (on my diagram) as a guide to make sure the easement doesn't stray too far.I start and end the easement 12 inches from where the curved track would meet the tangent track if there were no easement (original tangent).The offset is the distance the new tangent track is from where the original tangent track would be, measured outward. I use an offset of one inch, mostly because it looks good to me. You may want to use 1/2 inch.Then I put the piece of flextrack down so that it is even with (parallel to) the tangent track and the curve at the start and end points, and adjust until it looks like a smooth transition. The midpoint should be about halfway between the rails, but this isn't critical. What's important is that it looks smooth.Finally, I mark where the flextrack is located so I can lay permanent track in the right place.It's really very easy. None of the measurements is critical. I often use "one track width" instead of measuring one inch for the offset.A very important point is how easements change your layout. If you have an oval with 24-in radius curves, then your tangent tracks will be 48 inches center-to-center without easements. With easements the distance between tangent tracks will be greater by twice your offset. In my case that is 50 inches. As an alternative, in case your tangent track alignments are fixed, you can reduce the radius of your curve by the amount of the offset. Therefore, you have to take the offsets into account in the early planning phases.
This is really hard to grasp without a diagram, so I will give you a diagram.
I agree with Dave. I use a piece of flextrack to form the shape of the curve between the point on the tangent track and the point on the curve. I use the "midpoint" (on my diagram) as a guide to make sure the easement doesn't stray too far.
I start and end the easement 12 inches from where the curved track would meet the tangent track if there were no easement (original tangent).
The offset is the distance the new tangent track is from where the original tangent track would be, measured outward. I use an offset of one inch, mostly because it looks good to me. You may want to use 1/2 inch.
Then I put the piece of flextrack down so that it is even with (parallel to) the tangent track and the curve at the start and end points, and adjust until it looks like a smooth transition. The midpoint should be about halfway between the rails, but this isn't critical. What's important is that it looks smooth.
Finally, I mark where the flextrack is located so I can lay permanent track in the right place.
It's really very easy. None of the measurements is critical. I often use "one track width" instead of measuring one inch for the offset.
A very important point is how easements change your layout. If you have an oval with 24-in radius curves, then your tangent tracks will be 48 inches center-to-center without easements. With easements the distance between tangent tracks will be greater by twice your offset. In my case that is 50 inches. As an alternative, in case your tangent track alignments are fixed, you can reduce the radius of your curve by the amount of the offset. Therefore, you have to take the offsets into account in the early planning phases.
Thank you for that diagram. I THINK it is beginning to make sense. Please correct me if I am wrong, but when I start this excercise should I draw the tangent first, followed by the radius curve I am after ( let's say 24" dia ) then follow your advice and steps re the offset and easement ?
I really do appreciate all the advice that has been offered to me in this post.
Thank you all very much
Way too complicated.
I, likewise, set my curves 1/2" inside my tangents and then eyeball a a smooth curve between them. Unless you take a set of calipers to them they will be visually and operationally indistinguishable from the mathmatically calculated ones.
Dave H.
Dave H. Painted side goes up. My website : wnbranch.com